The board of Demoulas Super Markets Inc., owner of the Market Basket grocery chain, said it has instructed company management to open its long-stalled stores in Attleboro and Revere “at the earliest possible moment.”

But it’s unclear when that will be. Despite the go-ahead, management is at an “impasse” with the board on leasing issues and hasn’t decided when the stores will open, Market Basket director of operations Bill Marsden said.

“Unless those issues become resolved, things are status quo, to say the least,” he said.

The stores have been delayed by infighting between the Tewksbury chain’s board and management, including allegations that CEO Arthur T. Demoulas was involved in “self-dealing” real estate deals related to new sites that benefited his wife and brother-in-law. The board took over real estate decisions after a change in majority control last June that favors the CEO’s rival cousin, Arthur S. Demoulas.

Arthur T. Demoulas could not be reached for comment.

In a statement, a spokeswoman for the board said it has been “waiting patiently for many months for management to propose a plan and timetable to open the store in Attleboro. Management has not provided this plan, so the board has now instructed management to open the store … at the earliest possible moment.”

In March, Market Basket signed a lease for its new Waltham store, allowing work there — stalled since September — to proceed. New stores planned for Athol and Littleton are “on track,” according to the Demoulas board website.

The construction firm for Market Basket’s Attleboro store, which received a temporary occupancy permit in January, was granted a 90-day extension this week that expires Aug. 28. “I also let them know … that no further extensions would be granted,” Attleboro building commissioner Doug Semple said. There has been no communication with Market Basket “whatsoever,” he noted.

The Revere store was completed last July.

“The board … has been required to be actively involved in negotiating the lease of (the) property … given that the company’s CEO has a conflict of interest regarding the ownership and lease,” the board spokeswoman said.

The board previously approved the lease subject to certain conditions, which since have been satisfied, she said. “… The board …instructed management to sign the lease and … to open the store in Revere at the earliest possible moment,” she said.

Board chairman Keith Cowan declined comment. In a May 21 letter to Revere Mayor Daniel Rizzo, Cowan pointed to “deficiencies” in the Revere deal with “certain deed restrictions, site accessibility and the appropriateness of certain fees, charges and benefits.”

Earlier in the month, Rizzo wrote a letter to Cowan — which Cowan said he didn’t receive — saying that, “Having a brand new vacant and unused business facility was never part of my vision for economic growth” when he took office in 2012. “… I am turning this matter over to the city solicitor to explore whatever legal options may be at our disposal in order to rectify the situation we unfortunately find ourselves in,” Rizzo’s letter said.